Peristaltic Motion of Viscoelastic  Fluid with Fractional Second Grade Model in Curved Channels

Narla, V. K.; Prasad, K. Maruthi; Ramanamurthy, J. V.

doi:10.1155/2013/582390

Cited by 18 publications

(10 citation statements)

References 28 publications

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“…Figure 3(a) and (b) also reveals that significantly greater magnitudes for pressure rise are computed in the former as compared with the latter. The inverse pressure rise-flow rate relationship is also confirmed in both figures, concurring with numerous other non-Newtonian curved tube peristaltic studies, for example, Narla et al, 33 Kalantari 34 and Kalantari et al, 35 even though these other studies utilize different rheological models. Figure 4(a)-(c) presents the distributions for axial pressure gradient (dp/dx) with variation in flow rate (Q), curvature parameter (k) and upper limit apparent viscosity coefficient (b) plotted along the x-axis.…”

Section: Resultssupporting

confidence: 90%

Peristaltic transport of bi-viscosity fluids through a curved tube: A mathematical model for intestinal flow

Tripathi

Akbar

Khan

et al. 2016

Proc Inst Mech Eng H

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The human intestinal tract is a long curved tube constituting the final section of the digestive system in which nutrients and water are mostly absorbed. Motivated by the dynamics of chyme in the intestine, a mathematical model is developed to simulate the associated transport phenomena via peristaltic transport. Rheology of chyme is modelled using the Nakamura-Sawada bi-viscosity non-Newtonian formulation. The intestinal tract is considered as a curved tube geometric model. Low Reynolds number (creeping hydrodynamics) and long wavelength approximations are taken into consideration. Analytical solutions of the moving boundary value problem are derived for velocity field, pressure gradient and pressure rise. Streamline flow visualization is achieved with Mathematica symbolic software. Peristaltic pumping phenomenon and trapping of the bolus are also examined. The influence of curvature parameter, apparent viscosity coefficient (rheological parameter) and volumetric flow rate on flow characteristics is described. Validation of analytical solutions is achieved with a MAPLE17 numerical quadrature algorithm. The work is relevant to improving understanding of gastric hydrodynamics and provides a benchmark for further computational fluid dynamics (CFD) simulations.

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Section: Resultssupporting

confidence: 90%

Peristaltic transport of bi-viscosity fluids through a curved tube: A mathematical model for intestinal flow

Tripathi

Akbar

Khan

et al. 2016

Proc Inst Mech Eng H

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“…Ali et al 4 The above definition of stream function enables us to write Equations (17 -19) after using the long wavelength and low Reynolds number approximations (Kumar and Naidu 1995;Yi et al 2002;Takagi and Balmforth 2011;Hina et al 2013;Kalantari et al 2013;Narla et al 2013; …”

Section: Mathematical Model and Rheological Constitutive Equationsmentioning

confidence: 99%

“…They further noted that reflux close to the outer wall exhibits greater strength than near the inner wall and that the trapped bolus of fluid has two asymmetrical components, with the outer one growing and the inner one depleting as the channel curvature rises. The analysis by Sato et al (2000) has been extended by several researchers (Ali, Sajid, and Hayat 2010;Ali et al 2010aAli et al , 2010bHina et al 2013;Kalantari et al 2013;Narla et al 2013;) to a variety of nonlinear material and other effects including non-Newtonian behavior, unsteadiness, wall compliance etc. However, thus far no studies have appeared in the literature where peristaltic flow analysis in a curved channel is considered under long wavelength approximation for a fluid capable of predicting shear thinning, shear thickening, and relaxation effects.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of peristaltic flow of a biorheological fluid with shear-dependent viscosity in a curved channel

Ali

Javid

Sajid

et al. 2015

Computer Methods in Biomechanics and Biomedical Engineering

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Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n < 1) greater Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.

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“…The study performed by Sato et al 28 is pioneering in this direction. The results presented by Sato et al 28 were generalized by Ali et al, [29][30][31] Hayat et al, 32,33 Hina et al, [34][35][36] Ramanamurthy et al 37 and Narla et al 38 In this connection also the paper of Kalantari et al 39 is worth mentioning. It is related to those situation where the curvature of the channel, applied magnetic field and non-Newtonian effects are equally important.…”

Section: Introductionmentioning

confidence: 67%

Simulations of peristaltic slip-flow of hydromagnetic bio-fluid in a curved channel

2016

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The influence of slip and magnetic field on transport characteristics of a bio-fluid are analyzed in a curved channel. The problem is modeled in curvilinear coordinate system under the assumption that the wavelength of the peristaltic wave is larger in magnitude compared to the width of the channel. The resulting nonlinear boundary value problem (BVP) is solved using an implicit finite difference technique (FDT). The flow velocity, pressure rise per wavelength and stream function are illustrated through graphs for various values of rheological and geometrical parameters of the problem. The study reveals that a thin boundary layer exists at the channel wall for strong magnetic field. Moreover, small values of Weissenberg number counteract the curvature and make the velocity profile symmetric. It is also observed that pressure rise per wavelength in pumping region increases (decreases) by increasing magnetic field, Weissenberg number and curvature of the channel (slip parameter).

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Peristaltic Motion of Viscoelastic Fluid with Fractional Second Grade Model in Curved Channels

Cited by 18 publications

References 28 publications

Peristaltic transport of bi-viscosity fluids through a curved tube: A mathematical model for intestinal flow

Peristaltic transport of bi-viscosity fluids through a curved tube: A mathematical model for intestinal flow

Numerical simulation of peristaltic flow of a biorheological fluid with shear-dependent viscosity in a curved channel

Simulations of peristaltic slip-flow of hydromagnetic bio-fluid in a curved channel

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